Find segment df. picture will you.

Therefore the Segment DF is 7.2 unit.

Step-by-step explanation:

Given:

∠ABD ≅ ∠D

∠DCE ≅ ∠E

AC = 10

CE = 6

BD = 12

To Find:

DF = ?

Solution:

∠ABD ≅ ∠D .....Given

Which are Alternate Angles

AB || CD      ..........Alternate Angles Theorem

∠DCE ≅ ∠E ....Given

Which are Corresponding Angles

CD || EF       ............Corresponding Angles Theorem

Now we have,

If three or more parallel lines are cut by two transversals, then they divide the transversals proportionally.

AB || CD || EF cut by transversal BF and AE then

Substituting the values we get

Therefore the Segment DF is 7.2 unit.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

1. perpendicular

2. parallel

3. perpendicular